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NASA NTRS1992

Methods of testing parameterizations: Vertical ocean mixing

The ocean's velocity field is characterized by an exceptional variety of scales. While the small-scale oceanic turbulence responsible for the vertical mixing in the ocean is of scales a few centimeters and smaller, the oceanic general circulation is characterized by horizontal scales of thousands of kilometers. In oceanic general circulation models that are typically run today, the vertical structure of the ocean is represented by a few tens of discrete grid points. Such models cannot explicitly model the small-scale mixing processes, and must, therefore, find ways to parameterize them in terms of the larger-scale fields. Finding a parameterization that is both reliable and plausible to use in ocean models is not a simple task. Vertical mixing in the ocean is the combined result of many complex processes, and, in fact, mixing is one of the less known and less understood aspects of the oceanic circulation. In present models of the oceanic circulation, the many complex processes responsible for vertical mixing are often parameterized in an oversimplified manner. Yet, finding an adequate parameterization of vertical ocean mixing is crucial to the successful application of ocean models to climate studies. The results of general circulation models for quantities that are of particular interest to climate studies, such as the meridional heat flux carried by the ocean, are quite sensitive to the strength of the vertical mixing. We try to examine the difficulties in choosing an appropriate vertical mixing parameterization, and the methods that are available for validating different parameterizations by comparing model results to oceanographic data. First, some of the physical processes responsible for vertically mixing the ocean are briefly mentioned, and some possible approaches to the parameterization of these processes in oceanographic general circulation models are described in the following section. We then discuss the role of the vertical mixing in the physics of the large-scale ocean circulation, and examine methods of validating mixing parameterizations using large-scale ocean models.

Tziperman, Eli↗

NASA NTRS2013

Comparison of Four Precipitation Forcing Datasets in Land Information System Simulations over the Continental U.S.

The NASA Short ]term Prediction Research and Transition (SPoRT) Center in Huntsville, AL is running a real ]time configuration of the NASA Land Information System (LIS) with the Noah land surface model (LSM). Output from the SPoRT ]LIS run is used to initialize land surface variables for local modeling applications at select National Weather Service (NWS) partner offices, and can be displayed in decision support systems for situational awareness and drought monitoring. The SPoRT ]LIS is run over a domain covering the southern and eastern United States, fully nested within the National Centers for Environmental Prediction Stage IV precipitation analysis grid, which provides precipitation forcing to the offline LIS ]Noah runs. The SPoRT Center seeks to expand the real ]time LIS domain to the entire Continental U.S. (CONUS); however, geographical limitations with the Stage IV analysis product have inhibited this expansion. Therefore, a goal of this study is to test alternative precipitation forcing datasets that can enable the LIS expansion by improving upon the current geographical limitations of the Stage IV product. The four precipitation forcing datasets that are inter ]compared on a 4 ]km resolution CONUS domain include the Stage IV, an experimental GOES quantitative precipitation estimate (QPE) from NESDIS/STAR, the National Mosaic and QPE (NMQ) product from the National Severe Storms Laboratory, and the North American Land Data Assimilation System phase 2 (NLDAS ]2) analyses. The NLDAS ]2 dataset is used as the control run, with each of the other three datasets considered experimental runs compared against the control. The regional strengths, weaknesses, and biases of each precipitation analysis are identified relative to the NLDAS ]2 control in terms of accumulated precipitation pattern and amount, and the impacts on the subsequent LSM spin ]up simulations. The ultimate goal is to identify an alternative precipitation forcing dataset that can best support an expansion of the real ]time SPoRT ]LIS to a domain covering the entire CONUS.

Case, Jonathan L.↗

NASA NTRS2000

An Overview of the NCC Spray/Monte-Carlo-PDF Computations

This paper advances the state-of-the-art in spray computations with some of our recent contributions involving scalar Monte Carlo PDF (Probability Density Function), unstructured grids and parallel computing. It provides a complete overview of the scalar Monte Carlo PDF and Lagrangian spray computer codes developed for application with unstructured grids and parallel computing. Detailed comparisons for the case of a reacting non-swirling spray clearly highlight the important role that chemistry/turbulence interactions play in the modeling of reacting sprays. The results from the PDF and non-PDF methods were found to be markedly different and the PDF solution is closer to the reported experimental data. The PDF computations predict that some of the combustion occurs in a predominantly premixed-flame environment and the rest in a predominantly diffusion-flame environment. However, the non-PDF solution predicts wrongly for the combustion to occur in a vaporization-controlled regime. Near the premixed flame, the Monte Carlo particle temperature distribution shows two distinct peaks: one centered around the flame temperature and the other around the surrounding-gas temperature. Near the diffusion flame, the Monte Carlo particle temperature distribution shows a single peak. In both cases, the computed PDF's shape and strength are found to vary substantially depending upon the proximity to the flame surface. The results bring to the fore some of the deficiencies associated with the use of assumed-shape PDF methods in spray computations. Finally, we end the paper by demonstrating the computational viability of the present solution procedure for its use in 3D combustor calculations by summarizing the results of a 3D test case with periodic boundary conditions. For the 3D case, the parallel performance of all the three solvers (CFD, PDF, and spray) has been found to be good when the computations were performed on a 24-processor SGI Origin work-station.

Raju, M. S.↗

NASA NTRS1976

Statistical equilibrium calculations for silicon in early-type model stellar atmospheres

Line profiles of 36 multiplets of silicon (Si) II, III, and IV were computed for a grid of model atmospheres covering the range from 15,000 to 35,000 K in effective temperature and 2.5 to 4.5 in log (gravity). The computations involved simultaneous solution of the steady-state statistical equilibrium equations for the populations and of the equation of radiative transfer in the lines. The variables were linearized, and successive corrections were computed until a minimal accuracy of 1/1000 in the line intensities was reached. The common assumption of local thermodynamic equilibrium (LTE) was dropped. The model atmospheres used also were computed by non-LTE methods. Some effects that were incorporated into the calculations were the depression of the continuum by free electrons, hydrogen and ionized helium line blocking, and auto-ionization and dielectronic recombination, which later were found to be insignificant. Use of radiation damping and detailed electron (quadratic Stark) damping constants had small but significant effects on the strong resonance lines of Si III and IV. For weak and intermediate-strength lines, large differences with respect to LTE computations, the results of which are also presented, were found in line shapes and strengths. For the strong lines the differences are generally small, except for the models at the hot, low-gravity extreme of our range. These computations should be useful in the interpretation of the spectra of stars in the spectral range B0-B5, luminosity classes III, IV, and V.

Kamp, L. W.↗

NASA NTRS2021

Improved Estimates of Pentad Precipitation through the Merging of Independent Precipitation Datasets

Three independent, quasi-global, gridded datasets of precipitation (a rain gauge-based dataset, the satellite-only component of the NASA Integrated Multi-satellitE Retrievals for Global Precipitation Measurement mission [IMERG] Final Run precipitation product, and precipitation estimates derived from NASA Soil Moisture Active Passive [SMAP] soil moisture retrievals), are objectively combined into a single pentad precipitation dataset at 36-km resolution using a unique approach based on extended triple collocation. The quality of each of the four datasets is then evaluated against independent observations. When a global land surface model at 36-km resolution is integrated four times, once utilizing the merged precipitation forcing and once with each of the three contributing datasets, the near-surface soil moisture variations produced with the merged forcing validate best against independent satellite-based soil moisture fields. In addition, the merged dataset is found to be more consistent, relative to each contributor, with estimates of air temperature variations across the globe. The merged dataset thus appears to draw successfully on the complementary strengths of each contributor: the particularly high quality of the rain gauge-based dataset in areas of high gauge density, the more uniform accuracy across the globe of the IMERG data, and the moderate accuracy, particularly in semi-arid regions, of the soil moisture retrieval-based data. Plain Language Summary Obtaining measurements of precipitation across the globe can be challenging. Rain gauges in some ways provide the most accurate measurements, but gauges are absent in many parts of the world, and even where they exist, they only measure precipitation at the gauge itself and therefore may not provide an accurate large-scale average. Satellite-based estimates of precipitation largely overcome these problems, but such data have their own issues, notably a “snapshot” (rather than a time-average) character of the measurements and difficulty associated with interpreting the measured radiances in the presence of complex land surfaces. In the present paper, we use a novel approach to generate a “merged” dataset, one that optimally combines the gauge precipitation information and the satellite-based precipitation information with a third set of estimates derived from soil moisture retrievals. The merged precipitation dataset and each of the three contributors (aggregated here to 5-day averages at a spatial resolution of about 36-km) are then evaluated for consistency with independent geophysical fields. The merged dataset is found to perform best, a clear indication that it takes proper advantage of the complementary strengths of each contributor and, accordingly, that the presented approach for merging the different contributors is indeed viable.

Precipitation↗

NASA NTRS2015

Biomaterials Out of Thin Air: in Situ, On-Demand Printing of Advanced Biocomposites

Upmass is the single most significant limitation of our current space mission capability. Although biomaterials and biocomposites have mass, strength, flexibility, and self-healing properties that could significantly reduce upmass, their use is limited by the following drawbacks: Expensive, specific production. Many biomaterials can only be produced as part of significant support ecosystem; Inaccessible functional customization. The grain of wood, the porosity of bone, and so on are an integral part of the materials' desired mechanical properties, but are not deterministic when the material is naturally grown; Limited compositions. Most biomaterials (unlike metal, plastic, etc.) cannot be easily combined or modified to produce new materials. This project builds on recent advances in: Synthetic biology. Libraries of standardized genetic parts which can be used for controlled cellular material production, delivery, and binding; 3D printing. Commercial off-the-shelf components which can be used to make of a pico- to nanoliter cell deposition system; Tissue engineering. Proven cell-compatible support hydrogels and scaffolds can be modified to bind the deposited biomaterials of interest. Objectives: Feasibility and benefit analysis. Two mission contexts span the concept's scope (see below); Proof-of-concept demonstration. A simple grid of two proteins, fluorescent for easy detection, to validate the core technology concept; Proposed implementations for follow-on work. Avenues for future work on each core component (host cell, production control, material delivery, material binding, etc.); Complementary studies exploration. A survey of other emerging areas (in situ resource utilization, protein engineering, etc.) with the potential to multiply our technology's impact. Potential Impacts: This application could dramatically expand manufacturing capabilities on Earth and in space: In situ resource utilization. A far greater range of materials and products will be available from the limited palette offered by in situ resource extraction techniques; Reduced equipment and material upmass for off-Earth habitats. Ready- to-use highly specialized construction materials (radiation hardened, compressive/tensile, light or dense) from an extremely low starting mass; Structured biomaterial production. New ready-to-use macro, micro, and molecular manufacturing techniques for traditional biomaterials such as wood, bone and shell; New and novel biocomposite creation. The ability to create completely novel material composites from any base material that cells can be engineered to produce. Suggested Mission Contexts: ISS part manufacturing. A 'minimal working example' making a finished biomaterial part aboard the International Space Station; A long-term Mars habitat. 'Cradle-to-grave' use at a hypothetical Mars habitat, covering everything from tools to construction materials. Alternate Abstract: Imagine being able to print anything from tools and composite building materials to food and human tissues. Imagine being on Mars with the ability to replace any broken part, whether it's a part of your spacesuit, your habitat, or your own body. We propose a technique that would allow just that. By printing 3D arrays of cells engineered to secrete the necessary materials, the abundant in situ resources of atmosphere and regolith become organic, inorganic, or organic-inorganic composite materials. Such materials include novel, biologically derived materials not previously possible to fabricate.

habitats↗

NASA NTRS2015

Biomaterials Out of Thin Air: in Situ, On-demand Printing of Advanced Biocomposites

habitats↗

NASA NTRS2006

Can High-resolution WRF Simulations Be Used for Short-term Forecasting of Lightning?

A number of research teams have begun to make quasi-operational forecast simulations at high resolution with models such as the Weather Research and Forecast (WRF) model. These model runs have used horizontal meshes of 2-4 km grid spacing, and thus resolved convective storms explicitly. In the light of recent global satellite-based observational studies that reveal robust relationships between total lightning flash rates and integrated amounts of precipitation-size ice hydrometeors in storms, it is natural to inquire about the capabilities of these convection-resolving models in representing the ice hydrometeor fields faithfully. If they do, this might make operational short-term forecasts of lightning activity feasible. We examine high-resolution WRF simulations from several Southeastern cases for which either NLDN or LMA lightning data were available. All the WRF runs use a standard microphysics package that depicts only three ice species, cloud ice, snow and graupel. The realism of the WRF simulations is examined by comparisons with both lightning and radar observations and with additional even higher-resolution cloud-resolving model runs. Preliminary findings are encouraging in that they suggest that WRF often makes convective storms of the proper size in approximately the right location, but they also indicate that higher resolution and better hydrometeor microphysics would be helpful in improving the realism of the updraft strengths, reflectivity and ice hydrometeor fields.

Goodman, S. J.↗

NASA NTRS2011

Does Terrestrial Drought Explain Global CO2 Flux Anomalies Induced by El Nino?

The El Nino Southern Oscillation is the dominant year-to-year mode of global climate variability. El Nino effects on terrestrial carbon cycling are mediated by associated climate anomalies, primarily drought, influencing fire emissions and biotic net ecosystem exchange (NEE). Here we evaluate whether El Nino produces a consistent response from the global carbon cycle. We apply a novel bottom-up approach to estimating global NEE anomalies based on FLUXNET data using land cover maps and weather reanalysis. We analyze 13 years (1997-2009) of globally gridded observational NEE anomalies derived from eddy covariance flux data, remotely-sensed fire emissions at the monthly time step, and NEE estimated from an atmospheric transport inversion. We evaluate the overall consistency of biospheric response to El Nino and, more generally, the link between global CO2 flux anomalies and El Nino-induced drought. Our findings, which are robust relative to uncertainty in both methods and time-lags in response, indicate that each event has a different spatial signature with only limited spatial coherence in Amazonia, Australia and southern Africa. For most regions, the sign of response changed across El Nino events. Biotic NEE anomalies, across 5 El Nino events, ranged from -1.34 to +0.98 Pg Cyr(exp -1, whereas fire emissions anomalies were generally smaller in magnitude (ranging from -0.49 to +0.53 Pg C yr(exp -1). Overall drought does not appear to impose consistent terrestrial CO2 flux anomalies during El Ninos, finding large variation in globally integrated responses from 11.15 to +0.49 Pg Cyr(exp -1). Despite the significant correlation between the CO2 flux and El Nino indices, we find that El Nino events have, when globally integrated, both enhanced and weakened terrestrial sink strength, with no consistent response across events

Schwalm. C. R.↗

NASA NTRS2004

Three-Dimensional High-Order Spectral Volume Method for Solving Maxwell's Equations on Unstructured Grids

A three-dimensional, high-order, conservative, and efficient discontinuous spectral volume (SV) method for the solutions of Maxwell's equations on unstructured grids is presented. The concept of discontinuous 2nd high-order loca1 representations to achieve conservation and high accuracy is utilized in a manner similar to the Discontinuous Galerkin (DG) method, but instead of using a Galerkin finite-element formulation, the SV method is based on a finite-volume approach to attain a simpler formulation. Conventional unstructured finite-volume methods require data reconstruction based on the least-squares formulation using neighboring cell data. Since each unknown employs a different stencil, one must repeat the least-squares inversion for every cell at each time step, or to store the inversion coefficients. In a high-order, three-dimensional computation, the former would involve impractically large CPU time, while for the latter the memory requirement becomes prohibitive. In the SV method, one starts with a relatively coarse grid of triangles or tetrahedra, called spectral volumes (SVs), and partition each SV into a number of structured subcells, called control volumes (CVs), that support a polynomial expansion of a desired degree of precision. The unknowns are cell averages over CVs. If all the SVs are partitioned in a geometrically similar manner, the reconstruction becomes universal as a weighted sum of unknowns, and only a few universal coefficients need to be stored for the surface integrals over CV faces. Since the solution is discontinuous across the SV boundaries, a Riemann solver is thus necessary to maintain conservation. In the paper, multi-parameter and symmetric SV partitions, up to quartic for triangle and cubic for tetrahedron, are first presented. The corresponding weight coefficients for CV face integrals in terms of CV cell averages for each partition are analytically determined. These discretization formulas are then applied to the integral form of the Maxwell equations. All numerical procedures for outer boundary, material interface, zonal interface, and interior SV face are unified with a single characteristic formulation. The load balancing in a massive parallel computing environment is therefore easier to achieve. A parameter is introduced in the Riemann solver to control the strength of the smoothing term. Important aspects of the data structure and its effects to communication and the optimum use of cache memory are discussed. Results will be presented for plane TE and TM waves incident on a perfectly conducting cylinder for up to fifth order of accuracy, and a plane wave incident on a perfectly conducting sphere for up to fourth order of accuracy. Comparisons are made with exact solutions for these cases.

Liu, Yen↗

NASA NTRS2011

Estimating Evapotranspiration Using an Observation Based Terrestrial Water Budget

Evapotranspiration (ET) is difficult to measure at the scales of climate models and climate variability. While satellite retrieval algorithms do exist, their accuracy is limited by the sparseness of in situ observations available for calibration and validation, which themselves may be unrepresentative of 500m and larger scale satellite footprints and grid pixels. Here, we use a combination of satellite and ground-based observations to close the water budgets of seven continental scale river basins (Mackenzie, Fraser, Nelson, Mississippi, Tocantins, Danube, and Ubangi), estimating mean ET as a residual. For any river basin, ET must equal total precipitation minus net runoff minus the change in total terrestrial water storage (TWS), in order for mass to be conserved. We make use of precipitation from two global observation-based products, archived runoff data, and TWS changes from the Gravity Recovery and Climate Experiment satellite mission. We demonstrate that while uncertainty in the water budget-based estimates of monthly ET is often too large for those estimates to be useful, the uncertainty in the mean annual cycle is small enough that it is practical for evaluating other ET products. Here, we evaluate five land surface model simulations, two operational atmospheric analyses, and a recent global reanalysis product based on our results. An important outcome is that the water budget-based ET time series in two tropical river basins, one in Brazil and the other in central Africa, exhibit a weak annual cycle, which may help to resolve debate about the strength of the annual cycle of ET in such regions and how ET is constrained throughout the year. The methods described will be useful for water and energy budget studies, weather and climate model assessments, and satellite-based ET retrieval optimization.

Rodell, Matthew↗

NASA NTRS2017

A Hybrid Line List for CH4 and Hot Methane Continuum

Molecular line lists (a catalogue of transition frequencies and line strengths) are important for modelling absorption and emission processes in atmospheres of different astronomical objects, such as cool stars and exoplanets. In order to be applicable for high temperatures, line lists for molecules like methane must contain billions of transitions, which makes their direct (line-by-line) application in radiative transfer calculations impracticable. Here we suggest a new, hybrid line list format to mitigate this problem, based on the idea of temperature-dependent absorption continuum. Methods. The line list is partitioned into a large set of relatively weak lines and a small set of important, stronger lines. The weaker lines are then used either to construct a temperature-dependent (but pressure-independent) set of intensity cross sections or are blended into a greatly reduced set of super-lines. The strong lines are kept in the form of temperature independent Einstein A coefficients. Results. A line list for methane is constructed as a combination of 17 million strong absorption lines relative to the reference absorption spectra and a background methane continuum in two temperature-dependent forms, of cross sections and super-lines. This approach eases the use of large high temperature line lists significantly as the computationally expensive calculation of pressure dependent profiles only need to be performed for a relatively small number of lines. Both the line list and cross sections were generated using a new 34 billion methane line list (34 to10), which extends the 10to10 line list to higher temperatures (up to 2000 K). The new hybrid scheme can be applied to any large line lists containing billions of transitions. We recommend to use super-lines generated on a high resolution grid based on resolving power R = 1,000,000 to model the molecular continuum as a more flexible alternative to the temperature dependent cross sections.

Line Profiles↗

NASA NTRS1993

Semi-span model testing in the National Transonic Facility

A semi-span testing technique has been proposed for the NASA Langley Research Center's National Transonic Facility (NTF). Semi-span testing has several advantages including (1) larger model size, giving increased Reynolds number capability; (2) improved model fidelity, allowing ease of flap and slat positioning which ultimately improves data quality; and (3) reduced construction costs compared with a full-span model. In addition, the increased model size inherently allows for increased model strength, reducing aeroelastic effects at the high dynamic pressure levels necessary to simulate flight Reynolds numbers. The Energy Efficient Transport (EET) full-span model has been modified to become the EET semi-span model. The full-span EET model was tested extensively at both NASA LRC and NASA Ames Research Center. The available full-span data will be useful in validating the semi-span test strategy in the NTF. In spite of the advantages discussed above, the use of a semi-span model does introduce additional challenges which must be addressed in the testing procedure. To minimize the influence of the sidewall boundary layer on the flow over the semi-span model, the model must be off-set from the sidewall. The objective is to remove the semi-span model from the sidewall boundary layer by use of a stand-off geometry. When this is done however, the symmetry along the centerline of the full-span model is lost when the semi-span model is mounted on the wind tunnel sidewall. In addition, the large semi-span model will impose a significant pressure loading on the sidewall boundary layer, which may cause separation. Even under flow conditions where the sidewall boundary layer remains attached, the sidewall boundary layer may adversely effect the flow over the semi-span model. Also, the increased model size and sidewall mounting requires a modified wall correction strategy. With these issues in mind, the semi-span model has been well instrumented with surface pressure taps to obtain data on the expected complex flow field in the near wall region. This status report summarizes the progress to date on developing the semi-span geometry definition suitable for generating structured grids for the computational research. In addition, the progress on evaluating three state-of-the-art Navier-Stokes codes is presented.

Chokani, Ndaona↗

NASA NTRSDate not supplied

NASA/GEWEX SRB Surface Radiation Budget Fluxes Through the Prism of Weather States

The NASA/GEWEX Surface Radiation Budget Version 4 (SRB Rel4) product is now publicly available, covering the period from July 1983 through June 2017. This supersedes the SRB Rel3 (Stackhouse et al., 2011) product which has been used in the community for a wide variety of applications, including climate model validation, agriculture, solar energy, and architecture. SRB Rel4 uses the newly recalibrated and processed ISCCP HXS product as its primary input for cloud and radiance data, replacing ISCCP DX with a ninefold increase in pixel count (10km instead of 30km). This version retains a 1°x1° resolution but benefits from a much larger number of samples per grid box than the SRB Rel3. ISCCP also provides an atmospheric temperature and moisture dataset known as nnHIRS which we use here, along with Seaflux and Landflux surface and near-surface meteorological parameters. Rel4 incorporates several important algorithm improvements. These include recalculated shortwave (SW) atmospheric transmissivities and reflectivities yielding a somewhat less transmissive atmosphere. Both shortwave and longwave (LW) now also include variable aerosol composition and radiative properties, allowing for the use of a detailed aerosol history from the Max Planck Institute Aerosol Climatology (MACv1). LW and SW algorithms now produce pristine sky fluxes, allowing the aerosol flux effects to be quantified. For SW, ocean albedo and snow/ice albedo are improved from Release 3. Total solar irradiance is now variable, and reduced to an average of 1361 Wm-2. The radiative treatment of ice cloud is improved. For the LW, a climatological monthly varying spectral surface emissivity is added. Here we evaluate the SRB Rel4 top of atmosphere (TOA) and surface fluxes in the context of weather states and oceanic regions. Weather states (Tselioudis et al., 2013, Tselioudis et al., 2021) are defined by K-means clustering 2-D histograms of satellite-retrieved cloud optical depths and cloud top pressures. The most recent (Tselioudis et al., 2021) weather states derived from the International Satellite Cloud Climatology Project (ISCCP) H-series data results in eight cloud weather states and one clear sky weather state, for a total of nine weather states. We examine the statistics of SRB Rel4 fluxes for each weather state and a variety of relevant land and ocean regions. We compare to similar analyses performed on CERES EBAF and SYN1Deg flux products, and validate against Baseline Surface Radiometer Network (BSRN) land stations and Pacific Marine Environmental Laboratory (PMEL) ocean buoy data. It is demonstrated that the weather state concept is valuable when examining the comparative strengths and weaknesses of satellite radiative flux algorithms.

Atmospheric Radiation↗

NASA NTRS2015

Rao-Blackwellization for Adaptive Gaussian Sum Nonlinear Model Propagation

When dealing with imperfect data and general models of dynamic systems, the best estimate is always sought in the presence of uncertainty or unknown parameters. In many cases, as the first attempt, the Extended Kalman filter (EKF) provides sufficient solutions to handling issues arising from nonlinear and non-Gaussian estimation problems. But these issues may lead unacceptable performance and even divergence. In order to accurately capture the nonlinearities of most real-world dynamic systems, advanced filtering methods have been created to reduce filter divergence while enhancing performance. Approaches, such as Gaussian sum filtering, grid based Bayesian methods and particle filters are well-known examples of advanced methods used to represent and recursively reproduce an approximation to the state probability density function (pdf). Some of these filtering methods were conceptually developed years before their widespread uses were realized. Advanced nonlinear filtering methods currently benefit from the computing advancements in computational speeds, memory, and parallel processing. Grid based methods, multiple-model approaches and Gaussian sum filtering are numerical solutions that take advantage of different state coordinates or multiple-model methods that reduced the amount of approximations used. Choosing an efficient grid is very difficult for multi-dimensional state spaces, and oftentimes expensive computations must be done at each point. For the original Gaussian sum filter, a weighted sum of Gaussian density functions approximates the pdf but suffers at the update step for the individual component weight selections. In order to improve upon the original Gaussian sum filter, Ref. [2] introduces a weight update approach at the filter propagation stage instead of the measurement update stage. This weight update is performed by minimizing the integral square difference between the true forecast pdf and its Gaussian sum approximation. By adaptively updating each component weight during the nonlinear propagation stage an approximation of the true pdf can be successfully reconstructed. Particle filtering (PF) methods have gained popularity recently for solving nonlinear estimation problems due to their straightforward approach and the processing capabilities mentioned above. The basic concept behind PF is to represent any pdf as a set of random samples. As the number of samples increases, they will theoretically converge to the exact, equivalent representation of the desired pdf. When the estimated qth moment is needed, the samples are used for its construction allowing further analysis of the pdf characteristics. However, filter performance deteriorates as the dimension of the state vector increases. To overcome this problem Ref. [5] applies a marginalization technique for PF methods, decreasing complexity of the system to one linear and another nonlinear state estimation problem. The marginalization theory was originally developed by Rao and Blackwell independently. According to Ref. [6] it improves any given estimator under every convex loss function. The improvement comes from calculating a conditional expected value, often involving integrating out a supportive statistic. In other words, Rao-Blackwellization allows for smaller but separate computations to be carried out while reaching the main objective of the estimator. In the case of improving an estimator's variance, any supporting statistic can be removed and its variance determined. Next, any other information that dependents on the supporting statistic is found along with its respective variance. A new approach is developed here by utilizing the strengths of the adaptive Gaussian sum propagation in Ref. [2] and a marginalization approach used for PF methods found in Ref. [7]. In the following sections a modified filtering approach is presented based on a special state-space model within nonlinear systems to reduce the dimensionality of the optimization problem in Ref. [2]. First, the adaptive Gaussian sum propagation is explained and then the new marginalized adaptive Gaussian sum propagation is derived. Finally, an example simulation is presented.

state estimation↗